I see on IMDB that Kostal assumes a lot of hats. I suspect some of the orchestration is his, but I wouldn't be surprised if he didn't farm some of it out to friends, possibly Herb Spencer or Eddie Powell, or assistants who'd worked with him in Hollywod since MARY POPPINS.
Russell Bennett regularly used Joe Glover, Hans Spialek, and a few others when he got in a jam; Bill Brohn and Jonathan Tunick worked on the Lincoln Center SHOW BOAT with Bennett. On SOUND OF MUSIC, Rodgers told him that he wanted the entire score done by Bennett, and I suspect that was indeed the case.